The VG algebra tope-graph reconstruction conjecture

Assume $\operatorname{char} R\neq 2$. Let $\mathcal{A}_1$ and $\mathcal{A}_2$ be real arrangements. Their filtered VG algebras are $\operatorname{\mathcal{VG}}(\mathcal{A}_i)$, and their graded VG algebras are $\operatorname{\mathsf{VG}}^\bullet(\mathcal{A}_i)$. The VG algebra tope-graph reconstruction conjecture. If

$$\operatorname{\mathcal{VG}}(\mathcal{A}_1)\cong\operatorname{\mathcal{VG}}(\mathcal{A}_2)$$

as filtered algebras, or if

$$\operatorname{\mathsf{VG}}^\bullet(\mathcal{A}_1)\cong\operatorname{\mathsf{VG}}^\bullet(\mathcal{A}_2)$$

as graded algebras, then the tope graphs $\operatorname{\mathcal{T}}(\mathcal{A}_1)$ and $\operatorname{\mathcal{T}}(\mathcal{A}_2)$ are isomorphic. The conjecture would extend the result known in the supplied text for arrangements generic in codimension $2$ to general arrangements; the supplied text gives no resolution.